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Abstract

We present a theoretical analysis of the time-gated phase matching (ionization gating) mechanism in high-order harmonic generation for the isolation of attosecond pulses at near-infrared and mid-infrared driver wavelengths, for both few-cycle and multi-cycle driving laser pulses. Results of our high harmonic generation and three-dimensional propagation simulations show that broadband isolated pulses spanning from the extreme-ultraviolet well into the soft X-ray region of the spectrum can be generated for both few-cycle and multi-cycle laser pulses. We demonstrate the key role of absorption and group velocity matching for generating bright, isolated, attosecond pulses using long wavelength multi-cycle pulses. Finally, we show that this technique is robust against carrier-envelope phase and peak intensity variations.

Figures (4)

Optimal gas pressure, laser wavelength and pulse duration for generating bright isolated attosecond pulses. We show the attosecond pulse yields and temporal profiles as a function of the gas pressure of a 2-mm-helium-gas-cell for driving laser pulses of wavelength (λ) 0.8 μm (a)(d), 1.3 μm (b)(e) and 2 μm (c)(f) and temporal duration (τp) of 1.4 (front row) and 5.8 (back row) cycles FWHM respectively. The laser pulse is modeled by a sin2 envelope with a peak intensity chosen to match optimal phase matching conditions [22]. The yield in each lineout is divided by the gas pressure for the sake of clarity, and normalized to the yield of the attosecond pulse structure obtained at 5 torr.

Time gated phase-matching mechanism for the generation of soft X-ray isolated attosecond pulses. The time-frequency analysis of the high-harmonic radiation is shown for laser driving pulses of 0.8 μm (left column) and 2 μm (right column), and 5.8 cycles FWHM pulse duration. The pressure of the generating helium cell increases from (a) 5 torr to (e) 400 torr at 0.8 μm and from (b) 5 torr to (f) 150 torr at 2 μm. The time-frequency yield is normalized in each panel. Note that in agreement with theoretical prediction in Eq. (2), isolation of attosecond pulses occurs at lower pressures for the longer wavelength laser pulse.

Influence of group-velocity matching and absorption on the isolated attosecond pulse yields. We show the integrated yield of the central attosecond pulse as a function of gas pressure for a (a) multi-cycle (5.8) and (b) few-cycle (1.4) driving laser pulse of wavelengths 0.8 μm (red circles), 1.3 μm (green diamonds) and 2.0 μm (purple triangles). In panel (a) the dashed lines correspond to the simulations where absorption is not taken into account in the simulations. The yellow line represents the results of one-dimensional simulations at 2 μm for the sake of comparison. In panel (b), the dashed lines correspond to simulations where group velocity mismatch is not considered (absorption included), showing the relevance of group velocity walk off in the case of few-cycle laser pulses.

Robustness of the time-gated phase-matching isolation technique against carrier-envelope-phase and intensity variations. We present the yields and temporal profile of the harmonic emission generated at a gas pressure of 150 Torr with a λ = 2 μm, τp = 5.8 cycles laser pulse, as a function of (a) the carrier-envelope-phase ϕCEO and (b) the peak intensity of the driving laser pulse. This technique appears to be robust for variations over a rather wide range of carrier-envelope-phases (from ϕCEO = −π/4 to ϕCEO = π/4), and within intensity fluctuations of about ±2.5%.